[Insight-developers] level sets: curvature term and time step

[Lydia Ng]

Question for those interested in level sets:

Currently the itk::LevelSetFunction class does not take the curvature
term into account when computing the time step to meet the CFL criterion
to ensure numerical stability.

This is causing some grief with users playing around with the scaling
parameter in each of the term in particular when they set the curvature
scaling to be high relative to the propagation and advection terms.

Can someone point me to a paper/book that talks about have to compute
the CFL time step for the curvature term?=20

Alternatively, (hacking versus mathematically sound) could we just
restrict the time step such that the change in level set value due to
the curvature term is no larger that half a pixel? Would this have the
desired affect?

The second alternative is for me to change my filters
ShapeDetectionLevelSetImageFilter and
GeodesicActiveContourLevelSetImageFilter just to use a constant time
step - making it the user's problem to ensure they choose the time step
small enough. This is how it was before, when I got complaints from
other users about how it was difficult to set this parameter...

Cheers,
Lydia